Ab Initio Melting Temperatures of Bcc and Hcp Iron Under the Earth’s Inner Core Condition

• Published in: Geophysical research letters Vol. 50; no. 5
• Main Authors: Sun, Yang, Mendelev, Mikhail I., Zhang, Feng, Liu, Xun, Da, Bo, Wang, Cai‐Zhuang, Wentzcovitch, Renata M., Ho, Kai‐Ming
• Format: Journal Article
• Language: English
• Published: Washington John Wiley & Sons, Inc 16.03.2023; Wiley
• Subjects: ab initio calculation; Approximation; atomic‐scale simulation; Coexistence; Computer simulation; Earth; Earth core; Earth’s core; Energy; Free energy; Iron; Melt temperature; Melting; melting temperature; Size effects; Solid phases; Temperature; thermodynamic integration; Thermodynamics; Uncertainty
• ISSN: 0094-8276; 1944-8007
• DOI: 10.1029/2022GL102447

There has been a long debate on the stable phase of iron under the Earth’s inner core conditions. Because of the solid‐liquid coexistence at the inner core boundary, the thermodynamic stability of solid phases directly relates to their melting temperatures, which remains considerable uncertainty. In the present study, we utilized a semi‐empirical potential fitted to high‐temperature ab initio data to perform a thermodynamic integration from classical systems described by this potential to ab initio systems. This method provides a smooth path for thermodynamic integration and significantly reduces the uncertainty caused by the finite‐size effect. Our results suggest the hcp phase is the stable phase of pure iron under the inner core conditions, while the free energy difference between the hcp and bcc phases is tiny, on the order of 10 s meV/atom near the melting temperature. Plain Language Summary The structure of Earth’s solid inner core is a fundamental question in understanding the Earth’s interior. Fe is the major element in the Earth’s solid inner core, while its stable phase under inner core conditions is still under debate. The inaccuracy of present ab initio free energy calculations was too large to estimate the small free energy difference between different Fe phases, making this debate unsolved. In this paper, we developed a method to determine Fe’s melting temperatures from ab initio calculations. This was achieved by utilizing a potential fitted to high‐temperature ab initio data and performing a thermodynamic integration from classical systems described by this potential to ab initio systems. This method significantly reduces the uncertainty caused by the finite size effect in the ab initio calculations. Using this method, we calculated the free energy difference and melting temperatures of hcp and bcc Fe under inner‐core boundary and center conditions. We show that the hcp phase is the stable phase of pure Fe throughout the inner core condition. However, the bcc and hcp phases show a very small free energy difference that may be altered by other elements in the inner core. Key Points Thermodynamic integration with a potential fitted to high‐temperature ab initio data allows precise melting temperature determinations Hcp and bcc Fe’s melting temperatures are computed at the same ab initio accuracy at 323 and 360 GPa Bcc Fe is metastable while its free energy is only ∼10 meV/atom higher than the stable hcp phase under inner core conditions